Numerical simulations of the number of satellites in galaxy groups predict the presence of a huge number of dwarf galaxies [1]}. However, these predictions are not confirmed in observations. In fact, if the number of bright galaxies is in agreement with these predictions, the number of observed dwarfs is up to two orders of magnitude lower than expected [2]}. This is the so-called missing satellite problem.
[3]} pointed out that FGs could scale up the missing satellite problem at the mass scales of more massive galaxies. In particular, they compared the number of satellites predicted by \(\Lambda \) CDM at different halo mass scales and concluded that FGs shown smaller number of galaxies such as the Milky Way and the Large Magallanic Cloud than those predicted by the structure formation theory. They claimed that the reason of this lack of bright galaxies was due to over merging processes occurred in FGs. These early findings made FGs extreme objects in the structure formation of the Universe. The over merging processes in FGs could be explained in terms of differences in the orbital structure between fossil and non-fossil systems. [4]} used cosmological TreeSPH simulations to study the orbital structure of the intra-group (IG) stars for a set of clusters with masses \(\sim 10^{14}\)  M\(_{\odot }\) . He concluded that the velocity distribution of the IG stars was significantly more radially anisotropic for fossil than for non-fossil systems. This pointed out that the initial velocity distribution of the group galaxies could play an important role in defining the fossil status of the system.
